This project is based on the statistical problem of minimizing either of two metrics. Although these metrics differ simply in the placement of an exponent inside or outside an integral, they have considerably different applications. The first can be used to implement sampling, chi-square, nonparametric inferential, "age" adjustment, ridit transformation, distributional transformation and scale change, subcomponent isolation and editing and a large number of maximum likelihood procedures. The second metric can be used to obtain kernel and series density estimates with high resolution in low probability density regions.